Question

1.(x+1)/35 + (x+3)/33 = (x+5)/33 + (x+7)/20

2. (X+1)/12+ (X+2)/13 = (X+3)/14+ (X+4)/15

3. (X-85)/15+ (X-75)/13+(X-67)/11+ (X-64)/9=10

4. (X-1)/13-(2X-13)/15=(3X-15)/27- (4X-27)/29

Answer 1

x=-36

x=11

x=100

x=14

Answer 2

x=-36

x=11

x=100

x=14

Answer 3

2: \(\Leftrightarrow\left(\dfrac{x+1}{12}-1\right)+\left(\dfrac{x+2}{13}-1\right)=\left(\dfrac{x+3}{14}-1\right)+\left(\dfrac{x+4}{15}-1\right)\)

=>x-11=0

=>x=11

3: \(\Leftrightarrow\left(\dfrac{x-85}{15}-1\right)+\left(\dfrac{x-74}{13}-2\right)+\left(\dfrac{x-67}{11}-3\right)+\left(\dfrac{x-64}{9}-4\right)=0\)

=>x-100=0

=>x=100

Answer 4

\(\dfrac{x+1}{35}+\dfrac{x+3}{33}=\dfrac{x+5}{31}+\dfrac{x+7}{29}\)

\(\Rightarrow\left(\dfrac{x+1}{35}+1\right)+\left(\dfrac{x+3}{33}+1\right)=\left(\dfrac{x+5}{31}+1\right)+\left(\dfrac{x+7}{29}+1\right)\)

\(\Rightarrow\dfrac{x+36}{35}+\dfrac{x+36}{33}-\dfrac{x+36}{31}-\dfrac{x+36}{29}=0\)

\(\Rightarrow\left(x+36\right)\times\left(\dfrac{1}{35}+\dfrac{1}{33}-\dfrac{1}{31}-\dfrac{1}{29}\right)=0\)

\(\Rightarrow x+36=0\left(Vì\dfrac{1}{35}+\dfrac{1}{33}-\dfrac{1}{31}-\dfrac{1}{29}>0\right)\)

\(\Rightarrow x=-36\)